Effect of $K^0-{\bar{K}}^0$ Mixing on $CP$ Asymmetries in Weak Decays of $D$ and $B$ Mesons

Abstract

Within the standard electroweak model we carry out an instructive analysis of the effect of $K^0-{\bar{K}}^0$ mixing on $CP$ asymmetries in some weak decay modes of $D^{\pm }$ and $\stackrel{(-)}{B}$${}_d^0$ mesons. We point out that a clean signal of $CP$ violation with magnitude of 2Re($ϵ$) $\approx 3.3\times 10^{-3}$ can manifest in the semileptonic decays $D^{+}\to l^{+}{\nu }_l^{}{K}_S$ ($K_L$) vs $D^{-}\to l^{-}{\bar{\nu }}_l^{}{K}_S$ ($K_L$). The $CP$ asymmetries are also dominated by 2Re($ϵ$) in the two-body nonleptonic decays $D^{\pm }\to ({\pi }^{\pm },{\rho }^{\pm },a_1^{\pm })+(K_S,K_L)$ and in the multi-body processes $D^{\pm }\to {\pi }^{\pm }+n_0{\pi }^0+n_{\pm }({\pi }^{\pm }{\pi }^{\mp })+(K_S,K_L)$, where $n_0$ and $n_{\pm }$ are integers. It is possible to observe such $CP$-violating signals with about $10^7$ $D^{\pm }$ events at $\tau$-charm factories or hadron machines. Finally we show that the $CP$ asymmetry induced by Re($ϵ$) may compete with those from $B_d^0-{\bar{B}}_d^0$ mixing and final-state interactions in the semi-inclusive and exclusive decays $B_d\to X(c\bar{c})+(K_S,K_L)$ on the ${\rm Y}(4S)$ resonance.

Comments: 10 Latex pages + 2 figures. Phys. Lett. B (in printing)